Classical Mechanics Illustrated by Modern Physics

Integrable models have a fascinating history with many important discoveries that dates back to the famous Kepler problem of planetary motion. Nowadays it is well recognised that integrable systems play a ubiquitous role in many research areas ranging from quantum field theory, string theory, solvable models of statistical mechanics, black hole physics, quantum chaos and the AdS/CFT correspondence, to pure mathematics, such as representation theory, harmonic analysis, random matrix theory and complex geometry.

FACHGEB The last decade has seen a tremendous development in critical point theory in infinite dimensional spaces and its application to nonlinear boundary value problems. In particular, striking results were obtained in the classical problem of periodic solutions of Hamiltonian systems. This book provides a systematic presentation of the most basic tools of critical point theory: minimization, convex functions and Fenchel transform, dual least action principle, Ekeland variational principle, minimax methods, Lusternik- Schirelmann theory for Z2 and S1 symmetries, Morse theory for possibly degenerate critical points and non-degenerate critical manifolds.

FACHGEB The last decade has seen a tremendous development in critical point theory in infinite dimensional spaces and its application to nonlinear boundary value problems. In particular, striking results were obtained in the classical problem of periodic solutions of Hamiltonian systems. This book provides a systematic presentation of the most basic tools of critical point theory: minimization, convex functions and Fenchel transform, dual least action principle, Ekeland variational principle, minimax methods, Lusternik- Schirelmann theory for Z2 and S1 symmetries, Morse theory for possibly degenerate critical points and non-degenerate critical manifolds.

This series helps teachers demystify physics by showing students what it looks like. Field trips to hot-air balloon events, symphony concerts, bicycle shops, and other locales make complex concepts more accessible. Inventive computer graphics illustrate abstract concepts such as time, force, and capacitance, while historical re-enactments of the studies of Newton, Leibniz, Maxwell, and others trace the evolution of theories. The Mechanical Universe helps meet different students' needs, from the basic requirements of liberal arts students to the rigorous demands of science and engineering majors. This series is also valuable for teacher professional development.

This 2007 book presents the development of modern molecular models for fluids from the interdisciplinary fundamentals of classical and statistical mechanics, of electrodynamics and of quantum mechanics.